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114 lines
3.3 KiB
OCaml
114 lines
3.3 KiB
OCaml
(*
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copyright (c) 2013-2014, simon cruanes
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all rights reserved.
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redistribution and use in source and binary forms, with or without
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modification, are permitted provided that the following conditions are met:
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redistributions of source code must retain the above copyright notice, this
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list of conditions and the following disclaimer. redistributions in binary
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form must reproduce the above copyright notice, this list of conditions and the
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following disclaimer in the documentation and/or other materials provided with
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the distribution.
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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
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ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
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WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
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DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
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FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
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SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
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OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*)
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(** {1 Categorical Constructs}
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Attempt to copy some structures from Haskell and the likes. Disclaimer:
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I don't know much about category theory, only about type signatures ;). *)
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(** {2 Signatures} *)
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module type MONOID = sig
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type t
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val empty : t
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val append : t -> t -> t
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end
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module type FUNCTOR = sig
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type +'a t
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val map : ('a -> 'b) -> 'a t -> 'b t
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end
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module type APPLICATIVE = sig
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type +'a t
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include FUNCTOR with type 'a t := 'a t
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val pure : 'a -> 'a t
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val (<*>) : ('a -> 'b) t -> 'a t -> 'b t
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end
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module type MONAD_BARE = sig
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type +'a t
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val return : 'a -> 'a t
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val (>>=) : 'a t -> ('a -> 'b t) -> 'b t
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end
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module type MONAD = sig
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include MONAD_BARE
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include APPLICATIVE with type 'a t := 'a t
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end
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module type MONAD_TRANSFORMER = sig
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include MONAD
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module M : MONAD
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val lift : 'a M.t -> 'a t
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end
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(** Cheating: use an equivalent of "to List" with a sequence *)
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type 'a sequence = ('a -> unit) -> unit
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module type FOLDABLE = sig
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type 'a t
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val to_seq : 'a t -> 'a sequence
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end
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module type TRAVERSE = functor(M : MONAD) -> sig
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type +'a t
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val sequence_m : 'a M.t t -> 'a t M.t
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val fold_m : ('b -> 'a -> 'b M.t) -> 'b -> 'a t -> 'b M.t
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val map_m : ('a -> 'b M.t) -> 'a t -> 'b t M.t
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end
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(** The free monad is built by nesting applications of a functor [F].
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For instance, Lisp-like nested lists can be built and dealt with like this:
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{[
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module Lisp = CCCat.FreeMonad(CCList);;
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let l = Lisp.(inj [1;2;3] >>= fun x -> inj [x; x*2; x+100]);;
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]} *)
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module type FREE_MONAD = sig
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module F : FUNCTOR
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type +'a t =
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| Return of 'a
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| Roll of 'a t F.t
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include MONAD with type 'a t := 'a t
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val inj : 'a F.t -> 'a t
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end
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(** {2 Some Implementations} *)
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(** Implement the applicative and functor modules from only return and bind *)
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module WrapMonad(M : MONAD_BARE) : MONAD with type 'a t = 'a M.t
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module MakeFree(F : FUNCTOR) : FREE_MONAD with module F = F
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module MakeFreeFold(FM : FREE_MONAD)(Fold : FOLDABLE with type 'a t = 'a FM.F.t)
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: FOLDABLE with type 'a t = 'a FM.t
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